Properties of Real Numbers
Distributive Property
For any real numbers a, b, and c,
a(b + c) = ab + ac and (b + c)a = ba + ca.
Inverse Properties
For any real number a, there is a single real number – a such that
a + (-a) = 0 and –a + a = 0.
The inverse “undoes” addition with the result 0.
For any nonzero real number a , there is a single real number 
such that
a. = 1 and .a = 1.
The inverse “undoes” multiplication with the result 1.
Identity Properties
For any real number a , a + 0 = 0 + a = a.
Start with a number a; add 0. The answer is “identical” to a.
Also, a. 1 = 1. a = a.
Start with a number a; multiply by 1. The answer is “identical ” to a.
Commutative and Associative Properties
For any real numbers a, b, and c,
a + b = b + a
and ab = ba.
Commutative properties
Interchange the order of the two terms or factors.
Also, a + (b + c) = (a + b) + c
and a(bc) = (ab)c.
Associative properties
Shift parentheses among the three terms or factors; order stays the same.